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Chapter 4

Chapter 4. An introduction to molecular symmetry. 4.1 Introduction. Understanding of symmetry is essential in discussions of molecular spectroscopy and calculations of molecular properties. consider the structures of BF 3 , and BF 2 H , both of which are planar. BF bond distances

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Chapter 4

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  1. Chapter4 An introduction to molecular symmetry Dr. Said M. El-Kurdi

  2. 4.1 Introduction Understanding of symmetry is essential in discussions of molecular spectroscopy and calculations of molecular properties. consider the structures of BF3, and BF2H, both of which are planar BF bond distances are all identical (131 pm) trigonal planar the BH bond is shorter (119 pm) than the BF bonds (131 pm). pseudo-trigonal planar Dr. Said M. El-Kurdi

  3. the molecular symmetry properties are not the same Group theory is the mathematical treatment of symmetry. In this chapter, we introduce the fundamental language of group theory (symmetry operator, symmetry element, point group and character table). Dr. Said M. El-Kurdi

  4. 4.2 Symmetry operations and symmetry elements A symmetry operation is an operation performed on an object which leaves it in a configuration that is indistinguishable from, and superimposable on, the original configuration. The rotations are performed about an axis perpendicular to the plane of the paper and passing through the boron atom; the axis is an example of a symmetry element. Dr. Said M. El-Kurdi

  5. A symmetry operation is carried out with respect to points, lines or planes, the latter being the symmetry elements. Rotation about an n-fold axis of symmetry The symmetry operation of rotation about an n-fold axis (the symmetry element) is denoted by the symbol Cn, in which the angle of rotation is: n is an integer, e.g. 2, 3 or 4. Dr. Said M. El-Kurdi

  6. Applying this notation to the BF3 molecule BF3 molecule contains a C3 rotation axis Dr. Said M. El-Kurdi

  7. If a molecule possesses more than one type of n-axis, the axis of highest value of n is called the principal axis; it is the axis of highest molecular symmetry. For example, in BF3, the C3 axis is the principal axis. Dr. Said M. El-Kurdi

  8. Reflection through a plane of symmetry (mirror plane) If reflection of all parts of a molecule through a plane produces an indistinguishable configuration, the plane is a plane of symmetry Dr. Said M. El-Kurdi

  9. the symmetry operation is one of reflection and the symmetry element is the mirror plane (denoted by  ) • If the plane lies perpendicular to the vertical principal axis, it is denoted by the symbol h. • If the plane contains the principal axis, it is labeled v. Dr. Said M. El-Kurdi

  10. Consider the H2O molecule A special type of plane which contains the principal rotation axis, but which bisects the angle between two adjacent 2-fold axes, is labeled d Dr. Said M. El-Kurdi

  11. A square planar molecule: XeF4 One C2 axis coincides with the principal (C4) axis; the molecule lies in a h plane which contains two C2’ and two C2’’ axes. Dr. Said M. El-Kurdi

  12. Each of the two v planes contains the C4 axis and one C2’ axis. Dr. Said M. El-Kurdi

  13. Each of the two d planes contains the C4 axis and one C2’’ axis. In the notation for planes of symmetry, , the subscripts h, v and d stand for horizontal, vertical and dihedral respectively. Dr. Said M. El-Kurdi

  14. Reflection through a centre of symmetry (inversion centre) If reflection of all parts of a molecule through the centre of the molecule produces an indistinguishable configuration, the centre is a centre of symmetry, also called a centre of inversion; it is designated by the symbol i. CO2 benzene SF6 Dr. Said M. El-Kurdi

  15. No i H2S cis-N2F2 SiH4 Rotation about an axis, followed by reflection through a plane perpendicular to this axis If rotation through about an axis, followed by reflection through a plane perpendicular to that axis, yields an indistinguishable configuration, the axis is an n-fold rotation–reflection axis, also called an n-fold improper rotation axis. It is denoted by the symbol Sn. Dr. Said M. El-Kurdi

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  17. Identity operator All objects can be operated upon by the identity operator E. The operator E leaves the molecule unchanged. Dr. Said M. El-Kurdi

  18. 4.3 Successive operations For NH3 Dr. Said M. El-Kurdi

  19. For example, in planar BCl3, the S3 improper axis of rotation corresponds to rotation about the C3 axis followed by reflection through the h plane. Dr. Said M. El-Kurdi

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  21. Summary Table of Symmetry Elements and Operations Dr. Said M. El-Kurdi

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  24. 4.4 Point groups The number and nature of the symmetry elements of a given molecule are conveniently denoted by its point group C1 point group C1 = E Dr. Said M. El-Kurdi

  25. Cv point group -fold axis of rotation; that possessed by a linear molecule It must also possess an infinite number of v planes but no h plane or inversion centre. • These criteria are met by • Asymmetrical diatomics such as HF, CO and [CN], and • linear polyatomics that do not possess a centre of symmetry, e.g. OCS and HCN. Dr. Said M. El-Kurdi

  26. Dh point group • Symmetrical diatomics (e.g. H2, [O2]2) and • linear polyatomics that contain a centre of symmetry (e.g. [N3],CO2, HCCH) possess a h plane in addition to a C axis and an infinite number of v planes Dr. Said M. El-Kurdi

  27. Td, Oh or Ih point groups Molecular species that belong to the Td, Oh or Ih point groups possess many symmetry elements Dr. Said M. El-Kurdi

  28. Determining the point group of a molecule or molecular ion Dr. Said M. El-Kurdi

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  30. Determine the point group of trans-N2F2. Apply the strategy shown in Figure 4.10: Dr. Said M. El-Kurdi

  31. Determine the point group of PF5. Dr. Said M. El-Kurdi

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